Every April, one prospect gets hot and shoots up NFL draft boards, gathering momentum from unknown to dark horse to draft day surprise. This year it’s Tom Savage, the former Rutgers quarterback hyped as having the best arm in the class and touted as the hottest prospect on the board.

“The hottest guy in the draft,” Gil Brandt called him, before explaining to The Post exactly how and why the well-traveled college quarterback — who went from Rutgers’ highly-touted freshman phenom to forgotten man at Arizona to reclamation project at Pittsburgh — is rising in mock drafts and is expected to be a high second-round pick.

“He has adequate mobility. [He’s] not a fleet-footed guy, but [he’s]not slow,” Brandt added. “He has a great arm, reminds you of [Troy] Aikman with his accuracy and velocity on the ball. And he’s very smart, a quick learner. He’s got instant recall. This is one of those guys you ask him a question he answers it right away. I personally think he’s got a chance to be a very good quarterback.”

Brandt — the Cowboys vice president of player personnel, before becoming a SiriusXM radio analyst and NFL.com’s top personnel guru — isn’t alone in seeing Savage as a wild-card thrown into the draft pool of elite quarterbacks.

Initially forecasted as a fifth- or sixth-round pick, multiple scouts gush that he has “strongest arm in the draft,’’ and ESPN draft analyst Todd McShay tabs him going 33rd overall — the top pick in the second round, and Brandt has him No. 40 on his big board.

“Tom has a lot of talents,” ex-Rutgers and Buccaneers coach Greg Schiano told The Post. “He can make every throw. He has a big, sturdy frame, and he can see things pretty well,”

Which begs the questions: Why is he rising so quickly? And why now?

The answer lies in the twisting path he took.

Savage was a four-star prospect out of Springfield (Pa.) in 2009, Schiano’s biggest recruiting coup. He earned freshman All-American honors and team offensive MVP honors on a 9-4 Rutgers team that won the St. Petersburg Bowl.

But after taking a pounding as a sophomore, he hurt his hand and lost his job to Chas Dodd. When Schiano told Savage there would be an open competition for the job the next season, he left school — a decision a more mature Savage admitted at the recent NFL scouting combine was a mistake.

“I’d just stay at Rutgers, be patient, and earn my job back,” Savage said. “I got hurt. I lost my job. [Dodd] went in and played great for the team. Coach went with the hot hand. I was an 18-year-old kid, bitter and ticked off. I thought I had all the answers and decided to leave. Obviously, looking back now, I could’ve handled it a different way. But I definitely matured from the whole process. I grew from it.”

Savage said he needed to learn not to be so impulsive.

“Patience was one of the things I needed to learn at that age,” he said. “But you have early success and you don’t know why you have it. You think it’s easy and comes with the territory. Stick around, earn my spot back.

“Four years down the road, you learn from that.”

But Savage learned the hard way. He bolted for Arizona, sitting out a year while expecting to play in Mike Stoops’ pro-style offense; but when Rich Rodriguez came in to run the spread, Savage never suited up for the Wildcats.

He tried to transfer back to Rutgers, and Schiano was amenable, but when the NCAA denied his request to play immediately and Schiano left for the NFL, Savage ended up at Pittburgh, sitting out a second straight season.

“Tom and I have always been OK with each other, even when we were going through a tough situation,’’ Schiano told The Post. “We talked at the time when he left, we talked after [when he was looking to come back] and we’ve talked since. It’s a good relationship, and I think he’s going to be an excellent quarterback.”

Savage became just that at Pitt, completing 61.2 percent of his passes for 2,958 yards, 21 touchdowns and nine picks — just three in his last nine games as he shook off the rust from two years of inactivity.

At 6-foot-5, 230 pounds, Savage has prototype size. NFL personnel evaluate arm and accuracy, acumen and accountability. The first he always has had in abundance, the second is work in progress. Savage tends to stare down receivers, but he has played just 31 games, and Brandt calls him a quick study. Schiano said he sees the field well.

The wandering college career brings up legitimate questions about accountability, but Savage seemed to answer them as a senior.

As agent Neil Schwartz said, “He took ownership of what transpired at Rutgers,” and despite getting sacked an FBS-high 43 times at Pitt — including a fractured rib, bruised kidney and bloody urine at halftime of their bowl game — he never once threw his porous offensive line under the bus.

“Very strong arm, will put it where only the receiver can catch it, he’s a good leader now,” Brandt told The Post. “If he’d played four years at one school, he might be drafted in top half of the first round.”

That might be a reach, but Schwartz said there’s so much demand for private workouts — teams can host players and set up private workouts up to April 27, and still go see Savage at Pitt or his hometown right up until the May 8-10 draft — that Savage’s team actually had to turn a couple of away.

“Between the private workouts and the teams that came to Pitt, I’d say 24 or 25 teams [have shown interest],” Schwartz said. “It got to a point in time I had to tell two teams — not that he didn’t want to — but there was nothing left on the calendar,’’ said Schwartz, adding Savage has been invited to the draft.